Theorem 3eqtr2ri 2205

Description: An inference from three chained equalities. (Contributed by NM, 3-Aug-2006.) (Proof shortened by Andrew Salmon, 25-May-2011.)

Hypotheses

Ref	Expression
3eqtr2i.1	|- A = B
3eqtr2i.2	|- C = B
3eqtr2i.3	|- C = D

Assertion

Ref	Expression
3eqtr2ri	|- D = A

Proof of Theorem 3eqtr2ri

Step	Hyp	Ref	Expression
1		3eqtr2i.1	. . 3 |- A = B
2		3eqtr2i.2	. . 3 |- C = B
3	1, 2	eqtr4i 2201	. 2 |- A = C
4		3eqtr2i.3	. 2 |- C = D
5	3, 4	eqtr2i 2199	1 |- D = A

Syntax hints:   = wceq 1353

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-4 1510  ax-17 1526  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-cleq 2170

This theorem is referenced by:  funimacnv  5294  uniqs  6595  ef01bndlem  11766  cos2bnd  11770  sinhalfpilem  14251